A Liouville Problem for the Stationary Fractional Navier–Stokes–Poisson System

This paper deals with a Liouville problem for the stationary fractional Navier–Stokes–Poisson system whose special case k=0 covers the compressible and incompressible time-independent fractional Navier–Stokes systems in R^N≥2 . An essential difficulty raises from the fractional Laplacian, which is a non-local operator and thus makes the local analysis unsuitable. To overcome the difficulty, we utilize a recently-introduced extension-method in Wang and Xiao (Commun Contemp Math 18(6):1650019, 2016) which develops Caffarelli-Silvestre’s technique in Caffarelli and Silvestre (Commun Partial Diff Equ 32:1245–1260, 2007).